GS Chandy says:>A couple of years later, we had a math teacher who did not insist on mindless, 'by-rote' mugging, who tried to demonstrate that math could be very different indeed. I soon came to realise that math was, in fact, very beautiful and, in fact it was quite as exciting as any of the 'adventure stories' that I loved. In just a few months after that, I taught myself (with considerble help from that teacher) to pick up all the skills I needed to perform those 'multidigit, pencil-and-paper computations' that are involved in much 'math learning'. At this point, I began to find it a breeze - and I often did not even require pencil or paper: I could do a great many of the computations in my mind, often MUCH faster than my math teacher(s)!

That's interesting. You've had an experience like many have had, where some particular teacher out of the multitude strikes a resonant chord.

Can you say give a detail or two about a moment when you first started to feel this intellectual about-face?

I never hated math, but was bored in algebra. I had a 10th grade geometry teacher (we studied logic and Euclidean geometry exclusively.) He wasn't even a mathemetician per se, but a young law student. I think his youth had something to do with it, because it was his passion for logic that woke me up out of boredom more than anything. He also reminded me a bit of my cousin (a Phd. physicist at the time) -- also a big influence on me at the time.

So, my amusement in solving some math puzzles visually (impossible! according to Mr. Hansen) probably goes back to him as well. Like you I also began to practice mental calculation, just for fun (and it did and still does come in handy) and of course one does experience "personal algorithm creation" if you get far into that. I also tried "mental chess" with some friends but we could only get more than 8 moves or so in.